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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1296.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1296.c1 | 1296j1 | \([0, 0, 0, -99, -414]\) | \(-35937/4\) | \(-11943936\) | \([]\) | \(288\) | \(0.095341\) | \(\Gamma_0(N)\)-optimal |
| 1296.c2 | 1296j2 | \([0, 0, 0, 621, 594]\) | \(109503/64\) | \(-15479341056\) | \([]\) | \(864\) | \(0.64465\) |
Rank
sage: E.rank()
The elliptic curves in class 1296.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1296.c do not have complex multiplication.Modular form 1296.2.a.c
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
